Gabriela Kohr

Geometric Function Theory in One and Higher Dimensions

Univalent functions: elementary properties of univalent functions Subclasses of univalent functions in the unit disc The Loewner theory Bloch functions and the Bloch constant Linear invariance in the unit disc Univalent mappings in several complex variables and complex Banach spaces Univalence in several complex variables Growth, covering and distortion results for starlike and convex mappings in Cn and complex Banach spaces Loewner chains in several complex variables Bloch constant problems in several complex variables Linear invariance in several complex variables Univalent mappings and the Roper-Suffridge extension operator.

Univalent mappings associated with the Roper-Suffridge extension operator

The Roper-Suffridge extension operator provides a way of extending a (locally) univalent functionfεH(U) to a (locally) biholomorphic mappingF∈H(Bn). In this paper, we give a simplified proof of the Roper-Suffridge theorem: iff is convex, then so isF. We also show that iff∈S*, theF is starlike and that iff is a Bloch function inU, thenF is a Bloch mapping onBn. Finally, we investigate some open problems.

An Extension Theorem and Subclasses of Univalent Mappings in Several Complex Variables

Let B be the unit ball in C n and let U be the unit disc in C. The aim of this work is to construct a family of operators Ψ n,α that provide a way to extend a locally univalent function ƒ ∈ H(U) to a locally univalent mapping Fα ∈ H(B), where α ∈ (0,1]. If ƒ is normalized univalent, then Fα can be imbedded in a Loewner chain. Also if ƒ ∈ S*, then Fα is starlike. We show that if ƒ belongs to a class of univalent functions which satisfy growth and distortion results, then the mapping Fα satisfies similar growth and distortion results. Also we study the concept of linear-invariant families as it relates to families generated by the operator Ψ n,0, and we obtain in this way another example of a L.I.F. that has minimum order (n + 1)/2 and is not a subset of the normalized convex mappings in the unit ball of C n (for n ≤ 2.)

On some best bounds for coefficients of several subclasses of biholomorphic mappings in Cn

In this paper we obtain the best estimations for some coefficients of several subclasses of biholomorphic mappings defined on the unit ball of . As a consequence, we give some bounds for coefficients of starlike, starlike of order a e (0,1) and convex mappings on the unit ball of .

Growth and Distortion Results for Convex Mappings in Infinite Dimensional Spaces

In this paper, we obtain the growth result for normalized convex mappings on the unit ball of a complex Banach space. Also we give some bounds of coefficients and a distortion result for convex mappings on the unit ball of a complex Hilbert space.

Quasiconformal extension of biholomorphic mappings in several complex variables

AbstractLetf(z, t) be a subordination chain fort ∈ [0, α], α>0, on the Euclidean unit ballB inCn. Assume thatf(z) =f(z, 0) is quasiconformal. In this paper, we give a sufficient condition forf to be extendible to a quasiconformal homeomorphism on a neighbourhood of

KERNEL CONVERGENCE AND BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES

\bar B

Parametric representation and extension operators for biholomorphic mappings on some Reinhardt domains

. We also show that, under this condition,f can be extended to a quasiconformal homeomorphism of